Rules excluding various kinds of evidence from criminal trials play a prominent role in criminal procedure, and have generated considerable controversy. In this paper, we address the general topic of excluding factually relevant evidence, that is, the kind of evidence that would rationally influence the jury’s verdict if it were admitted. We do not offer a comprehensive analysis of these exclusionary rules, but add to the existing literature by identifying a new domain for economic analysis, focusing on how juries respond to the existence of such a rule. We show that the impact of exclusionary rules on the likelihood of conviction is complex and depends on the degree of rationality exhibited by juries and on the motivations of the prosecutor.